Lecture 11: Minimizing ‖x‖ Subject to Ax = b

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Description In this lecture, Professor Strang revisits the ways to solve least squares problems. In particular, he focuses on the Gram-Schmidt process that finds orthogonal vectors. Summary Picture the shortest \(x\) in \(\ell^1\) and \(\ell^2\) and \(\ell^\infty\) norms The \(\ell^1\) norm gives a sparse solution \(x\). Details of Gram-Schmidt orthogonalization and \(A = QR\) Orthogonal vectors in \(Q\) from independent vectors in \(A\) Related section in textbook: I.11 Instructor: Prof. Gilbert Strang